A toque (pron.: // or //) is a type of hat with a narrow brim or no brim at all. They were popular from the 13th to the 16th century in Europe, especially France. Now, it is primarily known as the traditional headgear for professional cooks.
The word Toque is Arabic "طوق" for "Round" and "طاقية" "Taqia" for "Hat" originally for something "Round" that has an opening. The word has been known in English since 1505. It came through the Medieval French toque (15th century), presumably by the way of the Spanish toca "woman's headdress", from Arabic *taqa'طاقة' 'Opening'.
Culinary use 
The toque most likely originated as the result of the gradual evolution of head coverings worn by cooks throughout the centuries. Their roots are sometimes traced to the casque a meche (stocking cap) worn by 18th-century French chefs. The colour of the casque a meche denoted the rank of the wearer. Boucher, the personal chef of the French statesman Talleyrand, was the first to insist on white toques for sanitary reasons. The modern toque is popularly believed to have originated with the famous French chefs Marie-Antoine Carême and Auguste Escoffier.
- A toque, or sometimes touge, was the traditional headgear of various French magistrates.
- A low type in black velvet, called mortier (also rendered in English as mortar board), was used by the président à mortier, president of a parlement (the royal highest court in a French province), and of the members of two of the highest central courts, cour de cassation and cour des comptes.
- A red toque is sometimes worn by German judges, primarily by justices on the Federal Constitutional Court.
In the Napoleonic era, the French first empire replaced the coronets of traditional ('royal') heraldry with a rigorously standardized system (as other respects of 'Napoleonic' coats of arms) of toques, reflecting the rank of the bearer. Thus a Napoleonic Duke used a toque with 7 ostrich feathers and 3 lambrequins, a Count a toque with five feathers and two lambrequins, a Baron three feathers and one lambrequin, a Knight only one ostrich feather (see Nobility of the First French Empire).
There is also an unproven theory that the design of the papal tiara would have been based on a toque.
Canadian usage 
In Canada, toque, or tuque (pron.: //), is the common name for a knitted winter hat, or watch cap (sometimes also called a beanie). The Canadian English term was assimilated from Canadian French tuque. Toque first appeared in writing around 1870.
The fashion is said to have originated with the coureurs de bois, French and Métis fur traders, who kept their woollen nightcaps on for warmth during cold winter days. Such hats are known in other English-speaking countries by a variety of names, including beanie (American), watch cap or stocking cap; the terms tuque and toque are unique to Canada and northern areas of the United States close to the Canadian border.